Multivariable Calculus Lecture 2 - Oxford Mathematics 1st Year Student Lecture

This is the second of four lectures we are showing from our 'Multivariable Calculus' 1st year course. In the lecture, Sarah's focus is on 'Multiple Integrals in 2D; Change of Variables and Jacobians'.
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): • Oxford Mathematics Stu...
All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.

[@ssnoc]

Watching this without one clue of what she’s talking about - Amazing how anyone understands this.

[@rosskious7084]

All a person needs to do is climb the ladder one rung at a time. Imagine them reading a book on introductory psychology and then reading and studying their way to the level of a bachelor's degree of understanding. The person then picks up a book at the beginning level of a graduate degree and starts reading this book. You might have some difficulty with the book, but your background lets you learn and understand at that level and complete it. If a person picks up a graduate-level book without the background to comprehend the subject, they will not understand it and wonder how anyone could. The human mind is a powerful thing, and it can ascend to great things - one step at a time. The Calculus (itself) is not hard at this level ( the theory) - no hard proofs (they are at a higher level). What makes calculus hard at the level of Green's Theorem and Stoke’s Theorem are NOT the Green’s and Stoke's theorems themselves. The hard part is that a person needs to draw upon all the mathematics you have learned before (potentially) to do the calculations - Line integrals, triple and double integrals, Parametric equations, Partial derivatives, Derivatives, Trigonometry, Geometry, and algebra. You have to be a master of all the previous learning. This need separates those who learned the math to pass the current test from the ones who were there to learn the math. ( Sorry for my poor writing skills and grammar. I love math, reading and problem solving, but HATE grammar and writing 🤡)

[@rosskious7084]

Absolutely beautiful! Love that you did the integration of the region using the X,Y plane and then did it using the polar. Rather than just showing the easy way and the reason for doing it the easy way, you showed them why and how the region works both ways. This is critical in truly understanding how to translate the region into the bounds of integration. I have seen people call green's theorem ( which is extremely easy) hard , just because they never mastered the Regions of double integrals.

[@JonathanLang-nu2lx]

I loved the last lecture! This one is also perfectly timed with my course, thanks!

[@NaeemIrum]

Love to see this lecture. I really enjoyed lecture 01. I hope this would be a compete series of lecture. ❤

[@MartinKohn-ux3uy]

Excellent lecture. Clear and to the point. I have to point out though that slither is a verb meaning to move like a snake. The word you want is sliver!

[@michaeldarmanis8477]

Please upload the whole series!

[@cemerdogmus1601]

awesome lecture

[@AmarKumarJr]

This was very helpful thank u mam

[@scottychen2397]

Dear Lecturer, Could you comment on the relationship between these line integrals and the so-called ‘line-integrals’ one exercises using ‘dz’ in complex analysis. Theres confusion regarding their relationship…. They do not appear to be the same kind of thing despite the implication that they are.

[@mitchjacobs7603]

Excellent explanation of the Jacobian

[@JupiterThunder]

"This r here is the Jacobian". 😄

[@mrk3661]

how did we calculate that in polar coordinates ds = rdrdØ ??

[@genixia]

The arc length is proportional to its radius because the circumference of a complete circle is r.2π. In polar coordinates that 2π represents sweeping the complete circle from the x axis back to the x axis. An arc that only sweeps theta radians has a length of r.theta. The area dA is thus r.dr.dtheta

[@JupiterThunder]

dA = r.d(theta) x dr

[@jej3451]

41:50 Why did you choose X and Y for your limits? That's confusing AF. For one thing, these don't represent x- and y-coordinates. For another thing, it is impossible to distinguish lowercase x and y from uppercase X and Y in handwriting. a and b, or even x₁ and x₂, would have been much clearer. 46:14 J, really? When you've already been using J to mean the Jacobian? SMH

[@jeffmilroy9345]

Does she teach physics too?

[@AmitKumar-ve7uf]

GOOD MORNING MA'AM

[@noorfatima1303]

get lost 🤣

[@invisibules]

Slivers!

[@genixia]

@15:45 wouldn't annulate slithers be a better description?

[@JupiterThunder]

An annulus _is_ a slither 😄

[@GPSPYHGPSPYH-ds7gu]

The Ma'am is super lecture now this lecture is clear but most focus clearly Almighty Allah and God chosen for Me Math and Physics Almighty Allah and God give me opportunity for double PhD Al PAZA

[@Shazaantaimoor]

Ameen 💖

[@briancox9357]

Allah doesn't exist

[@okarakoo]

Does she mean "sliver" every time she says or writes "slither"? Can some native English speaker comment, please?

[@JupiterThunder]

Native here. You're quite right. Bear in mind that people at Oxford are a bit weird.

[@queenlip6152]

Right from the start. Did she have to write down what she says as if they were the most important points? Tha's why students havj problems with mathematics. They are being misled by their teachers intq focusing on the unimportant points. I am already falling asleep!

[@Heleous281]

Lovely lecture.....but how many trees were killed in order to learn Jacobians! (if someone has a legit explanation, I genuinely would like to know why paper is used instead of a chalk/white board)

[@OxfordMathematics]

Don't worry, it is a whiteboard.

[@Heleous281]

@@OxfordMathematics wow, that's incredible. What material is it made of? (or if you have a link for more information I'd be grateful)

[@kylewaddle7592]

you are so damn stupid@@Heleous281

[@jej3451]

@@Heleous281Do you not see her erasing the board with a rag, probably 20 times in this video?

[@donmoore7785]

Do you not realize it IS a whiteboard? I mean, did you NOTICE it being erased with a cloth?

[@paulhammond8583]

Ah yes, elementary.

[@naeemtahir6434]

I don't know why the teachers using notes when they are teaching no need of notes

[@mitchjacobs7603]

I suspect it's because they don't want to leave out anything, maybe due to nerves or something like that. They clearly know the material forward and backwards though

[@JupiterThunder]

It's not so much the notes that are odd, it's that she writes down everything she says on the board. Personally I'd get a handout ready with the lecture summarised and hand that out. Then you can just write down the mathematical steps on the board.

[@kousik8042]

Again copying from note and reading loud?..... udhar bhi reservation se job lagta he dekhlo guys

[@davidbuckingham7492]

Very boring and unimpressive style of copying notes... not engaging at all. Hope our top unis have embraced some modern tech being centres of research. My lectures were like this in 1983! Come on, put some effort in.